Question

four mutually exclusive projects are being considered for a new 2 - mile jogging track. the life of the track is expected to be 80 years, and the sponsoring agencys marr is 11% per year. annual benefits to the public have been estimated by an advisory committee and are shown below. use the b - c method (incrementally) to select the best jogging track. perform the incremental b - c analysis. fill - in the table below. (round to two decimal places.) the best jogging track is alternative

Explanation:

Step1: Arrange alternatives in ascending order of initial cost

First, we arrange the alternatives \(B\) (\(\$53000\)), \(A\) (\(\$55000\)), \(C\) (\(\$61000\)), \(D\) (\(\$160000\)) in ascending order of initial cost.

Step2: Incremental B - C ratio calculation for \(A - B\)

The formula for the incremental B - C ratio (\(BC_{A - B}\)) is \(BC_{A - B}=\frac{B_{A}-B_{B}}{P_{A}(A/P, i, n)-P_{B}(A/P, i, n)}\).
Since \(n = 80\) years and \(i=11\%\), \((A/P,11\%,80)\approx0.11\) (using the formula \((A/P,i,n)=\frac{i(1 + i)^{n}}{(1 + i)^{n}-1}\), and for large \(n\), when \(i = 0.11\), \((A/P,11\%,80)\approx0.11\)).
\(B_{A}-B_{B}=9500 - 8000=\$1500\), \(P_{A}(A/P, i, n)-P_{B}(A/P, i, n)=(55000 - 53000)\times0.11=\$220\)
\(BC_{A - B}=\frac{1500}{220}\approx6.82\)

Step3: Incremental B - C ratio calculation for \(C - A\)

\(B_{C}-B_{A}=10500 - 9500=\$1000\), \(P_{C}(A/P, i, n)-P_{A}(A/P, i, n)=(61000 - 55000)\times0.11=\$660\)
\(BC_{C - A}=\frac{1000}{660}\approx1.52\)

Step4: Incremental B - C ratio calculation for \(D - C\)

\(B_{D}-B_{C}=19000 - 10500=\$8500\), \(P_{D}(A/P, i, n)-P_{C}(A/P, i, n)=(160000 - 61000)\times0.11=\$10890\)
\(BC_{D - C}=\frac{8500}{10890}\approx0.78\)

Answer:

The best jogging track is alternative \(C\)